How to do PoseBone.children?
The children attribute is a convenience property, That is to say - Blender doesn't store a list of children for each bone, This attribute has just been added to some types since its such a common task.

Objects have this, but as you have noticed, not pose bones.

This can be monkey-patched in with:

import bpy

def pose_bone_children(self):
    obj = self.id_data
    pbones = obj.pose.bones
    self_bone = self.bone
    return tuple(pbones[bone.name] for bone in obj.data.bones
                 if bone.parent == self_bone)

# Add the property to the class at runtime
bpy.types.PoseBone.children = property(pose_bone_children)


Note that this will be included in 2.69, Committed r60407